0,4

A. P. Heinz (1990). Analyse der Grenzen und Moeglichkeiten schneller Tableauoptimierung. PhD Thesis, Albert-Ludwigs-Universitaet Freiburg, Freiburg i. Br., Germany.

Alois P. Heinz, Table of n, a(n) for n = 0..100

a(n) = A135429(n) - A135312(n).

a(3)=16 because there are 16 relations of the given kind for 3 elements:

1R2, 2R1, 1R3, 3R1, 2R3, 3R2;

1R2, 1R3, 2R3, 3R2;

2R1, 2R3, 1R3, 3R1;

3R1, 3R2, 1R2, 2R1;

1R2, 2R1, 1R3, 2R3;

1R3, 3R1, 1R2, 3R2;

2R3, 3R2, 2R1, 3R1;

1R2, 2R3, 1R3;

1R3, 3R2, 1R2;

2R1, 1R3, 2R3;

2R3, 3R1, 2R1;

3R1, 1R2, 3R2;

3R2, 2R1, 3R1;

1R2, 1R3;

2R1, 2R3;

3R1, 3R2;

(the reflexive relationships 1R1, 2R2, 3R3 have been omitted for brevity)

with (combinat, stirling2); A006882:= proc(n) option remember; if n<=1 then 1 else n*A006882(n-2); fi; end; A025035:= proc(n) option remember; (3*n)! /n! /(6^n); end; z:= proc(n) option remember; add (binomial (n, k+k) *A006882(k+k-1) *k^(n-k-k), k=0..floor(n/2)); end; r:= proc(n) option remember; n! * add (add (add (add (stirling2(e, d) *a^(d+i) *(a*(a+1)/2)^(n-i-i-e-d-a) /a! /(n-i-i-e-d-a)! /i! /e! /(2^i), a=0..(n-i-i-e-d)), d=0..min(e, n-i-i-e)), e=0..(n-i-i)), i=0..floor(n/2)); end; A135429:= proc(n) option remember; n! *add (add (A025035(i) *z(j) *r(n-3*i-j) /(3*i)! /j! /(n-3*i-j)!, j=0..(n-3*i)), i=0..floor(n/3)); end; A000248:= proc(n) add (binomial(n, i)*(n-i)^i, i=0..n); end; A135312:= proc(n) option remember; add (binomial(n, i+i)*A006882(i+i-1)*A000248(n-i-i), i=0..floor(n/2)); end; a:= proc(n) A135429(n)-A135312(n) end; seq(a(i), i=0..30);

Cf. A135429, A135312, A025035, A008277, A006882, A007318, A000248, A000142.

Sequence in context: A125379 A126537 A155657 this_sequence A000486 A006420 A049351

Adjacent sequences: A135455 A135456 A135457 this_sequence A135459 A135460 A135461

nonn

Alois P. Heinz (heinz(AT)hs-heilbronn.de), Dec 15 2007